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Abstract

Most existing differential phase-contrast computed tomography (DPC-CT) approaches are based on three kinds of scanning geometries, described by parallel-beam, fan-beam and cone-beam. Due to the potential of compact imaging systems with magnified spatial resolution, cone-beam DPC-CT has attracted significant interest. In this paper, we report a reconstruction method based on a back-projection filtration (BPF) algorithm for cone-beam DPC-CT. Due to the differential nature of phase contrast projections, the algorithm restrains from differentiation of the projection data prior to back-projection, unlike BPF algorithms commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a micro-focus x-ray tube source. Moreover, the numerical simulation and experimental results demonstrate that the proposed method can deal with several classes of truncated cone-beam datasets. We believe that this feature is of particular interest for future medical cone-beam phase-contrast CT imaging applications.

Figures (5)

Schematic geometry of x-ray refraction in a medium for cone-beam DPC-CT. (x′, z′) represents the index of detector channel. OAC is the central plane. D is the distance from the source to the rotation center O. γ represents the view angle under which the data was taken. l is any incident ray in the three dimensional space under γ. P is the line integral of δ along l.

Schematic representation of the cone-beam DPC-CT BPF algorithm. The sample slice in question is illustrated by green solid straight lines that are parallel to each other. L(γ) is the distance from the reconstructed point (x, y, z) to the x-ray source focus at view angle γ.
γ1γ2¯ is the horizontal straight line through the reference point (x, y, 0). OtAtCt is the tilted plane through the reconstructed point (x, y, z). Dt is the distance from the x-ray source focus to the rotation center Ot in the tilted plane. The reconstruction of the point (x, y, z) only needs the data taken in the angular range [γ1γ2] marked by the yellow curve. ϑ is the full cone-beam angle.

Four cases of truncated data resolved by the cone-beam DPC-CT BPF algorithm. The blue regions are the areas that can be reconstructed. (a) illustrates that the entire field of view can be reconstructed if the scanning angular range is larger than π + ϑ. (b) illustrates that a local region of interest (ROI) can be reconstructed if the scanning angular range is smaller than π + ϑ. (c) illustrates that a local ROI can be reconstructed if the projections are truncated to a smaller view angle. (d) illustrates that the imaging field of view can be enlarged if the detector is asymmetrically placed.

Numerical simulation results for the cases in Fig. 3. (a), (c), (e) and (g) are the truncated DPC datasets with sizes 256 × 256 × 191, 256 × 256 × 185, 200 × 200 × 360 and 138 × 256 × 360 pixels respectively. (b), (d), (f) and (h) are the 3D visualization of the corresponding DPC-CT images reconstructed with the BPF algorithm that is expressed by Eq. (1). We cut some part of the sample, which is indicated by the red curves in (b), to show the internal structure.

Experimental results. Sub-panels I, II, III and IV are corresponding to the cases in Figs. 3(a)–3(d) respectively. First columns in sub-panels are the truncated DPC datasets with sizes 560 × 1110 × 315, 560 × 1110 × 307, 200 × 1110 × 600 and 290 × 1110 × 600 pixels respectively. Second columns display the typical axial and sagittal slices reconstructed by Eq. (1). Third and forth columns show the orthogonal view slices and 3D rendering of the DPC-CT images respectively. We cut some part of the sample, which is indicated by the red curves, to show the internal structure.